Class X Science / Electricity

Key Notes

Electricity

Current:

I = Q/t, Where I = Current

Q = Net charge flowing.

t = time

• Unit:

The unit of current is Ampere.

Q = Coulomb(C)

I = Ampere(A)

t = Second(s) 1 A = 1C/1s

Potential Difference:

The potential difference between two separate points is defined as the work done to move a unit positive charge from one point to another.

V = W/Q

• Unit:

The unit of potential difference is Volt

1 Volt = 1 Joule/ 1 Coulomb

Ohm’s Law:

Current ∝ potential difference

V ∝ I

V = I R where, R = Resistance

• Unit:

R = Ω(Ohm)

1Ω = 1V / 1 A

• Factors on which resistance depends:

○ R ∝ 1, when A and material constant l = length

○ R ∝ 1/ A, when l and material constant A = perpendicular cross-section

R ∝l / A,

R = ρl / A, where ρ = resistivity

• Resistivity: Resistivity of a substance is equal to the resistance of a unit square of that substance.

Its Unitis Ωm.

Resistance in a series connection:

R = R1 + R2 + R3 + … + Rn

Resistance in parallel:

Heating Effect of current:

Electric energy = VIt

Heat, H = VIt = I2Rt

• Application:

Electric iron, toaster, fused wire, etc.

Fused wire: a low-melting point wire connected in series with electric devices for safety.

Electric power:

P = VI = I2R = V2/ R

• Unit: 1 kWh = 3.6 × 106J

1 W = 1V × 1A

Ohm’ law: Under constant physical conditions (i.e., constant temperature, pressure etc.), the current flowing through a conductor is directly proportional to the potential difference across the conductor.

Potential difference (which is measured in Voltage) is the cause of current (which is measured in Ampere).

In conductors, flow of electrons constitute current. In a circuit current flow from positive terminal of the battery to the negative terminal, but electrons travels from negative terminal to the positive terminal. The negative terminal of a battery is said to be at lower potential and the positive terminal is said to be at higher potential.

When a battery is not connected to any circuit, the potential difference across the terminals of the battery is equal to the EMF of the battery. (EMF = Electro Motive Force). Electromotive force, also called EMF, (denoted and measured in volts), refers to voltage generated by a battery or by the magnetic forceaccording to Faraday's Law, which states that a time varying magnetic field will induce an electric current.

Class X Science
NCERT Solutions For Electricity

Q1. What does an electric circuit mean?

Ans. A continuous conducting path consisting of wires and other resistances and a switch between the two terminals of a cell or a battery along which an electric current flow is called a circuit.

Q2. Define the unit of current.

Ans. The unit of current is Ampere. 1 Ampere is said to be when 1 coulomb of charge flow through any cross section of a conductor in 1 second.

Q3. Calculate the number of electrons constituting one coulomb of charge.

Ans. 1C = 6 × 1018 electrons.

Q4. Name a device that helps to maintain a potential difference across a conductor.

Ans. A battery of many cells or a single cell can maintain potential difference.

Q5. What is meant by saying that the potential difference between two points is 1 V?

Ans. The potential difference between two points is said to be 1 V if 1 Joule of work is done in moving 1 Coulomb of charge from one point to another point.

Q6. How much energy is given to each coulomb of charge passing through a 6 V battery?

Ans. Amount of charge = 1 coulomb or 1C

Potential difference = 6V

Energy or work done = ?

Work done or energy = V × Q[Q is the amount of charge flowing between two points at potential difference V = 6]

i.e., W = V × Q

W = 6 × 1

Work done or energy = 6 joules.

Q7. On what factors do the resistance of a conductor depend?

Ans. Resistance of a conductor depends on:

(a) Length of a conductor. Resistance of a conductor is directly proportional to the length of a conductor. If length increases resistance will also increase.

(b) Area of cross section of a conductor. The resistance of a conductor is inversely proportional to the area of the cross section of a conductor.

E.g. The resistance of nichrome wire is 60 times more than that of copper wire as nichrome has high electrical resistance.

(d) Effect of temperature. The resistance of all pure metals increases on increasing the temperature and decreases on decreasing the temperature.

Q8. Will current flow more easily through a thick wire or a thin wire of the same material, when connected to the same source? Why?

Ans. The current will flow more easily through a thick wire as compared to the thin wire because the resistance of thick wire is less than that of thin wire. Less resistance, means more current.

Q9. Let the resistance of an electrical component remains constant while the potential difference across the two ends of the component decreases to half of Us fanner value. What change will occur in the current through it?

Ans. Amount of current will be halved.

Q10. Why are coils of electric toasters and electric irons made of an alloy rather than a pure metal?

Ans. The coils of such heating appliances are made up of an alloy rather than a pure metal because:

(a) The resistivity of an alloy is much higher than that of a pure metal.

(b) An alloy does not undergo oxidation easily even at high temperature when it is even red hot.

Q11. (a) Which among iron and mercury is a better conductor?

(b) Which material is the best conductor?

Ans. (a) Iron

(b) Silver

Q12. Draw a schemata: diagram of a circuit consisting of a battery of three cells of 2 V each, a 5 Ω LI resistor, 8 Ω resistor, and a 12 Ω resistor, and a plug key, alt connected in seriess.

Ans.

Q13. Redraw the circuit of Question 12, putting in an ammeter to measure the current through the resistors and a voltmeter to measure the potential different across the 12 Ω resistors. What would be the readings in the ammeter and the voltmeter?

Rs = 5 Ω + 8 Ω + 12 Ω = 25 Ω

V = 6 V

I = ?

= 0.24 A

When R = 12 Ω

V = IR

= 0.24 x 12

= 2.88 V

Hence, reading in the ammeter would be 0.24 A and reading in voltmeter would be 2.88 V

Q14. Judge the equivalent resistance when Die following are connected in parallel—

(a) 1 Ω , 106 Ω , (b) 1 Ω , 103 Ω and 106 Ω.

Ans. (a) 1 ohm and 106 times ohm

R1 = 1 ohm

R2 = 106 times = 1000000 ohm

Total resistance in parallel 1/R = 1/R1 + 1/R2

= 1/1 + 1/1000000

= 1000000+1/1000000

= 1000001/1000000

= 1/R = 1/1 ohm (approx)

Resistance = 1 ohm (approx)

(b) R1 = 1 ohm

R2 = 103 ohm

R3 = 106 ohm

Total resistance in parallel

Q15. An electric lamp of 100 Ω, a toaster of resistance. 50 Ω , and a water filter of resistance 500 Ω are connected in parallel to a 220 V source. What is the resistance of an electric iron connected to the same source that takes as much current as all the three appliances, and what is the current through it?

Ans. Resistance of electric lamp =100 ohm

Resistance of a toaster = 50 ohm

Resistance of a water filter = 500 ohm

Potential difference = 220 volt

Total resistance of the three appliances in parallel = 1/R = 1/R1 + 1/R2 + 1/R3

= 1/100 + 1/50 + 1/500

1/R = 5 + 10 + 1/500

1/R = 16/500 = 4/125

= 125/4 = 31.25 ohm

V = I × R

220 = I × 31.25

I = 7.04 amp

Hence current through the electric iron = 7.04 amp.

Q16. What are the advantages of connecting electrical devices in parallel with the battery instead of connecting them in series?

Ans. Advantages of parallel connection are:

(a) In parallel circuit, if one electric appliance stop working due to some defect, then all other appliances keep working normally.

(b) In parallel circuit, each electrical appliance has its own switch due to which they can be turned on or off without affecting other appliances.

(d) In parallel connection of electrical appliances, the overall resistance of the circuit is reduced due to which the current from the power supply is high.

Q17. How can three resistors of resistances 2 Ω , 3 Ω , and 6 Ω be connected to give a total resistance of (a) 4 Ω , (b) 1 Ω?

Ans. R1 = 2 ohm

R2 = 3 ohm

R3 = 6 ohm

(a) When R2 and R3 are connected in parallel with R1 in series we get

1/R = 1/R2 + 1/R3

g= 1/3 + 1/6

= 1/2

Thus, R = 2 ohm

Resistance in series = R + R1

= 2 + 2

= 4 ohm

(b) When R1,R2, R3 are connected in parallel we get

1/R = 1/R1 + 1/R2 + 1/R3

= 1/2 + 1/3 + 1/6

= 1 ohm.

Q18. What is (a) the highest, (b) the lowest total resistance that can be secured by combinations of four coils of resistance 4 Ω , 8 Ω , 12 Ω , 24 Ω?

Ans. (a) The highest resistance is when the resistances are connected in series:

R1 = 4 ohm R2 = 8 ohm

R3 = 12 ohm R4 = 24 ohm

Total resistance in series = R1 + R2 + R3 + R4

= 4 + 8 + 12 + 24

= 48 ohm

Thus, highest resistance is 48 ohm.

(b) The lowest resistance is when the resistances are connected in parallel

Total resistance in parallel

= 1/R1 + 1/R2 + 1/R3 + 1/R4

1/R = 1/2 + 1/8 + 1/12 + 1/24

= 12/24

1/R = 1/2 ohm, R = 2 ohm

Thus, lowest resistance is 2 ohm.

Q19. Why does the cord of an electric heater no, glow while the heating element does?

Ans. The resistance of cord is extremely small as compared to that of heating element, so the heat produced in cord is less as compared to heating element. So the heating element begins to glow but cord does not glow.

Q20. Compute the heat generated while transferring 96000 coulomb of charge in one hour through a potential difference of 50 V.

Ans. Charge = 96000 coulomb

Time = 1 hour = 3600 seconds

Potential difference = 50 V

I = Q/T

I = 96000/3600 = 80/3 amp

V = I × R

50 = 80/3 × R

Thus. R = 15/8 ohm

Heat = I2RT

= (80/3)2 × 15/8 × 3600

= 800 × 6000

= 4800000 joules.

Q21. An electric iron a, resistance 20 Ω takes a current of 5 A Calculate the heat developed in 30 s.

Ans. Resistance of the iron = 20 ohm

Current = 5 amp

Time = 30 seconds

Heat produced = I2RT

= 52 × 20 × 30

= 15000 joules

Q22. What determines the rate at which energy is delivered by a current?

Ans. Electrical power determines the rate at which the energy is delivered by a current.

Q23. An electric motor takes 5 A from a 220 V line. Determine the power of the motor and the energy consumed in 2h.

Ans. Current in the motor, I = 5 amp

Potential difference, V = 220 V

Time = 2 hours

Power of the motor = V × I

= 220 × 5

1100 watt or 1.1. kWh

Energy = power × time

= 1.1 kWh × 2 h.

= 2.2 kWh

QUESTIONS FROM NCERT TEXTBOOK

Q1. A piece of wire of resistance R is cut into five equal parts. ‘These parts are then connected in parallel. If the equivalent resistance of this combination is R’, then what is the ratio R/R’?

Ans. 25 : 1

Q2. Which of the following terms does not represent electrical power in a circuit?

(a) I2R

(b) IR2

(d) V2/R

Ans. (b) IR2

Q3. An electric bulb is rated 220 V and 100 W. When it is operated on 110 V, power consumed will be—

(a) 100 W

(b) 75 W

(d) 25 W

Ans. (d) 25 W.

Q4. Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combinations would be—

(a) 1 : 2

(b) 2 : 1

(d) 4 : 1

Ans. (c) 1 : 4

Q5. How is a voltmeter connected in the circuit to measure the potential difference between two points?

Ans. It is connected in parallel.

Q6. A copper wire, has diameter 0.5 mm and resistivity of 1.6 × 10V8 Ω m. What will be the length of this wire to make its resistance 10 Ω ? How much does the resistance change if the diameter is doubled?

Ans. Diameter = 0.5 mm = 0.0005 m

The resistance becomes one-fourth if the diameter is doubled.

Q7. The values of current I flowing in a circuit with resistor for the corresponding values of potential difference V across the resistors are given below:

I (amperes) 0.5 1.0 2.0 3.0 4.0

V(volts) 1.6 3.4 6.7 10.2 13.2

Plot a graph between V and I and calculate the resistance of that resistor.

Ans.

Resistance of resistor R (mean)

Q8. When a 12 V battery is connected across an unknown resistor, there is a current 2.5 inA in the circuit. Find the value of the resistance of the resistor.

Ans. V = 12 V

I = 2.5 mA = 2.5 x 10-3 A

Q9. A battery of 9 V is connected in series with resistors of 0.2 Ω , 0.3 Ω , 0.4 Ω , 0.5 Ω and 12 Ω respectively. How much current would flow through the 12 Ω resistor?

Ans. V = 9 Y

Rs = 0.2 Ω + 0.3 Ω . + 0.4 Ω + 0.5 Ω + 12 Ω.

= 13.4 Ω

I = ?

Q10. How many 176 Ω resistors (in parallel) are required to carry 5 A on a 220 V line?

Ans. I = 5 A V = 220 V

Let the number of 176 Ω resistors be n.

Hence, four resistors of 176 W are required to carry 5 A on a 220 V line.

Q11. show how you would connect three resistors each of resistance 6 Ω , so that the combination has a resistance of (i) 9 Ω , (U) 4 Ω.

Ans. (i) To get 9 Ω ï¿½XConnect 2 resistors of 6 Ω in parallel and third resistor in series.

(ii) To get 4 Ω —Connect 2 resistors in series and the third in parallel to both of them

Q12. Several electric bulbs designed to be used on a 220 V electric supply line, are rata 10 W. How many lamps can be connected in parallel to each other across (he two win. of a 220 V line if the maximum allowable current is 5 A?

Ans. P = 10 W

If number of bulbs connected to current of 5 A is n. Then,

n = 5 ï¿½ 22 = 110

110 bulbs can be attached.

Q13. A hot plate of an electric oven connected to a 220 V line has two resistance coils A and B, each of 24 Ω resistance, which may be used separately, in series, or in parallel. What are the currents in the three cases?

Ans. (i) When used separately

(ii) When connected in series

(iii) When connected in parallel

Q14. Compare the power used in the 2 Ω resistor in each of the following circuits:

(i) a 6 V battery in series with 1 Ω and 2 Ω resistors, and

(ii) a 4 V battery in parallel with 12 Ω and 2 Ω resistors.

Ans. (i) V = 6 V

R1 = 1 Ω series with R3 = 2 Ω . P = ?

R2 = 2 Ω

R = R1 + R2 + R3

=1 + 2 = 30

Comparison: Power used by 2 Ω resistor in both the circuits are same, i.e. 8 W.

Q15. Two lamps, one rated 100 W at 220 V, and the other rated 60 W at 220 V, are connected in parallel to electric mains supply. What current is drawn from the line if the supply voltage is 220 V?

Ans. P1 = 100 w

P2 = 60 W

P = P1 + P2 = 160 W

V = 220 V

I = ?

Q16. Which uses more energy, a 250 W TV set in 1 hr, or a 1200 W toaster in 10 minutes?

Ans. 250 W TV set in an hour

Q17. An electric heater of resistance 8 Ω draws 15 A from the service mains for 2 hours. Calculate the rate of which heat is developed in. the heater

Ans. 1800 Wall.

Q18. Explain the following:

(a) Why the tungsten a used almost exclusively for the filament of electric lamps?

Ans. • It has a special property that it glows on heating.

• It has ,i high melting point.

• It does not tenet with the gases present in air and does not get oxidized.

• It has a low resistance.

(b) Why are the conductors of electric heating devices, such as bread-toasters and electric irons, made up of alloys rather than a pure menu?

Ans. • They offer higher resistance than pure metals, thus heating better.

• They have a high melting point.

• They do not oxidize.

Ans. • If any appliance is at fault, then the current is not able to flow through.

• Different appliances have different current requirements, but in series the current is the same. This can cause a power surge, thus damaging the appliances.

• Very long wires m domestic series circuits offer unusually high resistance, which is unwanted.

(d) How does the resistance of a wire vary with its area of cross section?

Ans. The relation between the resistance of a wire and its area of cross-section can be defined as:

• R is inversely proportional to the area of cross-section

(e) Why copper and aluminium wires are usually employed for electricity transmission?

Ans. • Copper and aluminium are much more easily and cheaply available than other metals.

• They offer low resistance and do not get heated.

• They can be easily made into wires due to high malleability.

MCQ for Electricity

1. What is the rate of flow of electric charges called?

(a) Electric potential

(b) electric conductance

(d) none of these

2. Which of the following is the SI Unit of Electric Current?

(a) ohm

(b) ampere

(d) faraday

3. Which instrument is used for measuring electric potential?

(a) Ammeter

(b) galvanometer

(d) potentiometer

4. When one unit electric charge moves from one point to another point in an electric circuit, then the amount of work done in joules is known as?

(a) Electric current

(b) electric resistance

(d) potential difference

5. The hindrance presented by material of conductor to the smooth passing of electric current is known as:

(a) Resistance

(b) Conductance

(d) None of these

6. The resistance of a conductor is directly proportional to:

(a) Its area of cross-section

(b) density

(d) length

7. The purpose of a rheostat is:

(a) Increase the magnitude of current only

(b) Decrease the magnitude of current only

(d) None of these

8. Point to be kept in mind for verification of Ohm’s Law is:

(a) Ammeter and voltmeter should be connected in series

(b) Ammeter should be connected in series and voltmeter in parallel

(d) Ammeter and voltmeter should be connected in parallel

9. When a 40V battery is connected across an unknown resistor there is a current of 100 mA in the circuit. Find the value of the resistance of the resister:

(a) 5000 Ω

(b) 800 Ω

(d) none of these

10. A battery of 6V is connected in series with resisters of 0.1 ohm , 0.15 ohm,0.2 ohm,0.25 ohm and 6 ohm. How much current would flow through the 0.3 ohm resistor?

(a) 0.895A

(b) 2.22A

(d) none of these

11. A fuse wire is inserted in a?

(a) . Live wire

(b) . In the neutral wire

(d) . May be connected inany line.

Sample Paper
Electricity

Two Mark Questions

1. Name the unit of (a) electrical resistance (b) resistivity

2. Define One Ohm

3. Define Resistivity

4. Determine the direction of conventional current?

5. What is electrical power? Write its unit.

Three Mark Questions

6. You take two resistors of resistance 2R and 3R and connect them in parallel in an electric circuit. Calculate the ratio of the electrical power consumed by 2R and 3R?

7. A small bulb has a resistance of 2Ω when cold. It takes up a current of 0.4 A from a source of 4V and then starts glowing. Calculate (i) the resistance of the bulb when it is glowing and

(ii) Elaborate on the reason for the difference in resistance?

8. Define resistance and resistivity and also give the relation between them. Explain the dependence of resistance on temperature.

9. A bulb is rated at 330V- 110W. What do you think is its resistance? Three such bulbs burn for 5hrs at a stretch. What is the energy consumed? Calculate the cost in rupees if the rate is 70 paise per unit?

10. Calculate the resistance of 2 km long copper wire of radius 2 mm. (Resistivity of copper = 1.72 x 1 0-8)

11. What connection is used in domestic appliances and why?

12. A 250 watt electric bulb is lighted for 5 hours daily and four 6 watt bulbs are lighted for 4.5 hours daily. Calculate the energy consumed (in kWh) in the month of February.

13. A torch bulb is rated at 3V and 600mA. Calculate it’s

(a) Power b) Resistance c) Energy consumed if it is lighted for 4 Hrs.

14. State and derive joule’s law. An electric iron consumes energy at rate of 420w when heating is at maximum rate and 180 w when heating is at minimum. The voltage is 220V .What is the current and resistant in each case?

15. A piece of wire having a resistance R is cut into five equal parts.

(i) How will the resistance of each part of the wire compare with the original resistance?

(ii) If the five parts of the wire are placed in parallel, how will the resistance of the combination compare with the resistance of the original wire? What will be ratio of resistance in series to that of parallel?

High Ordered Thinking Skills
Electricity

1. What is the difference between a conductor and an insulator?

2. What is the difference between open and closed circuits? Draw diagrams for both.

3. Define parallel connection and series connection.

4. What are the disadvantages of heating effect of current?

5. What are the advantages of heating effect of current?

6. What is electric current?

7. What is potential difference? Give its unit with definition.

8. Find the expression for calculating heat.

9. A wire is 1m long, 0.2mm in diameter and has resistance of 10Ω. Calculate its resistivity.

10. Calculate the area of cross section of a wire of length 2m, its resistance is 25Ω and the resistivity of material of wire is 1.84*10-6 Ωm.

11. Calculate the energy consumed by 120W toaster in 20 minutes.

12. What is resistance of conductors? Name two metals which are highly resistant.

13. Why is tungsten metal used in bulbs but not in fuse wires?

14. Define the terms Watt and Volt.

Test
Electricity

Time: 60 Minutes

MM- 35

Question 1 (1.0 marks)

What are the two types of electric charges?

Question 2 (1.0 marks)

What do you understand by potential difference?

Question 3 (1.0 marks)

The direction of current is the same as that of the flow of electrons. Explain with a circuit diagram. Is this statement true or false?

Question 4 (2.0 marks)

State Ohm’s law.

Question 5 (2.0 marks)

a) Calculate the energy transferred when 2 A current flows through a 10 Ω resistor for 30 minutes.

b) Calculate the amount of charge that would flow in one hour through the element of an electric iron drawing a current of 0.4 amps.

Question 6 (2.0 marks)

Draw a circuit diagram showing a cell, a bulb and a closed switch.

Question 7 (2.0 marks)

a) How much work is done in moving a charge of 3 coulumb from a point at the volts 115 to a point at 125 volts?

b) Ammeter burns out when connected in parallel. Give reasons.

Question 8 (2.0 marks)

Given n resistors each of resistors Rs. How will you combine them to get the ( I ) maximum and (ii) minimum effective resistance? What is the ratio of the maximum to minimum resistance?

Question 9 (3.0 marks)

a) A wire of length L and resistance R is stretched so that its length it’s doubled. How will the (a) Resistance change (b) Resistivity change?

b) In an experiment the current flowing through a resistor and potential difference across it are measured. The values are given below. Show that these values confirm Ohm’s Law

I (ampere) 1.0 1.0 2 1.5 2.0 2.0 2.5 2.5 3.0 3.0

V (volt) 4.0 4.0 6.0 6.0 8.0 8.0 10.0 10.0 12.0 12.0

Question 10 (3.0 marks)

a) A tube light draws 0.1 A current from a 220 V supply. What current will this tube light draw when it is connected to a 110 V supply?

a) An electric wire is stretched to increase its length by 25%.By what % will the resistance be increased and what will be increase in its resistivity?

Question 11 (3.0 marks)

a) Two resistances of 4 Ω and 8 Ω are connected in parallel. What would be the combined resistance of the system?

b) Two identical resistors each of resistance 2 Ohm are connected in turn (1) in series (2) in parallel to a battery of 12 V. Calculate the ratio of power consumed in two cases.

Question 12 ( 3.0 marks)

a) A household uses the following electric appliances:

(i) Refrigerator of rating 400 W for ten hours each day.

(ii) Two electric fans of rating 80 W each for twelve hours each day.

(iii) Six electric tubes of rating 18 W each for 6 hours each day.

Calculate the electricity bill of the household for the month of June if the cost per unit of electric energy is Rs. 3.00.

b) An electric iron of resistance 20Ωtakes a current of 5 A. Calculate the heat developed in 30sec.

Question 13 ( 5.0 marks)

a) Derive the expression for Joulesï¿½ law of heating.

b) Derive a formula for four equivalent resistances connected in series.

Question 14 ( 5.0 marks)

(a) The electric power consumed by a device may be calculated by using either of the two expressions P = 12R or P =V2/R . The first expression indicates that it is directly proportional to R whereas the second expression indicates inverse proportionality. How can the seemingly different dependence of P on R in these expressions be explained?

(b) (i) A 100 W electric bulb is connected to 220 V mains power supply. Calculate the strength of the electric current passing through the bulb. (ii) If the same bulb is taken to U.S.A where the main power supply is 110 V, how much electric current will pass through the bulb when connected to mains?

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